How many horizontal tangents does the graph of f(x)=(x-1)^2(x-3)^2 have?

Question

f(x)=(x-1)^2(x-3)^2

=2(x-1)(1)+2(x-3)(1)
=2x-2+2x-6

f'(x)=4x-8

0=4x-8
=4(x-2)

x=2

Therefore it only has 1 horizontal tangents?